# Dilute-Bose-Gas Approach to ground state phases of 3D quantum helimagnets under high magnetic field

## TL;DR

This paper uses a dilute Bose gas approach to analyze the ground state phases of 3D quantum helimagnets under high magnetic fields, revealing three distinct phases including a spin-nematic phase with 2-magnon BEC.

## Contribution

It extends the dilute Bose gas method to handle 2-magnon bound states, enabling the identification of a spin-nematic phase in 3D helimagnets.

## Key findings

- Identified three phases: cone, coplanar fan, and spin-nematic.
- Mapped the phase diagram of a frustrated J1-J2-J3 chain system.
- Extended BEC approach to include 2-magnon bound states.

## Abstract

We study high-field phase diagram and low-energy excitations of three-dimensional quantum helimagnets. Slightly below the saturation field, the emergence of magnetic order may be mathematically viewed as Bose-Einstein condensation (BEC) of magnons. The method of dilute Bose gas enables an unbiased quantitative analysis of quantum effects in three-dimensional helimagnets and thereby three phases are found: cone, coplanar fan and an attraction-dominant one. To investigate the last phase, we extend the usual BEC approach so that we can handle 2-magnon bound states. In the case of 2-magnon BEC, the transverse magnetization vanishes and long-range order occurs in the quadrupolar channel (spin-nematic phase). As an application, we map out the phase diagram of a 3D helimagnet which consists of frustrated J1-J2 chains coupled by an interchain interaction J3.